A question about UEqn sonicFoam

lfgmarc · July 14, 2012, 21:25

Hi, I have a question about the UEqn implemented into sonicFoam, the code of the UEqn is:

Code:

fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
    + fvm::div(phi, U)
    + turbulence->divDevRhoReff(U)
);

My question is about the term that is computed from the turbulence model, i.e if K-epsilon model is selected, this term results:

Code:

tmp<fvVectorMatrix> kEpsilon::divDevRhoReff(volVectorField& U) const
{
    return
    (
      - fvm::laplacian(muEff(), U)
      - fvc::div(muEff()*dev2(fvc::grad(U)().T()))
    );
}

Initially I thought that it corresponded to

$\nabla \cdot \left( \widetilde{\tau}-\bar{\rho}\widetilde{u^{''}u^{''}} \right) = 2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) +\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) - \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right) (1)$

but after examining the definition of dev2 in src/OpenFOAM/primitives/Tensor/TensorI.H

I found the following:

$dev2(u)=u-\frac{2}{3}tr\left(u\right)$

is the rate-of-strain tensor given by

$S=\frac{1}{2}\left(\nabla u + \left(\nabla u \right)^\mathrm{T} \right)$

but according to the definition of DivDevRhoReff

$divDevRhoReff = -\nabla^{2}\left(\mu_{eff} U\right) -\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)$

And manipulating the expression (1) I conclude that the term

Code:

     + turbulence->divDevRhoReff(U)

does not correspond to (1).

If someone can help me with my confusion about this term, I was very thankful

haze_1986 · January 24, 2013, 13:26

Quote:

Originally Posted by lfgmarc

Hi, I have a question about the UEqn implemented into sonicFoam, the code of the UEqn is:

Code:

fvVectorMatrix UEqn
(
    fvm::ddt(rho, U)
    + fvm::div(phi, U)
    + turbulence->divDevRhoReff(U)
);

My question is about the term that is computed from the turbulence model, i.e if K-epsilon model is selected, this term results:

Code:

tmp<fvVectorMatrix> kEpsilon::divDevRhoReff(volVectorField& U) const
{
    return
    (
      - fvm::laplacian(muEff(), U)
      - fvc::div(muEff()*dev2(fvc::grad(U)().T()))
    );
}

Initially I thought that it corresponded to

$\nabla \cdot \left( \widetilde{\tau}-\bar{\rho}\widetilde{u^{''}u^{''}} \right) = 2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) +\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) - \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right) (1)$

but after examining the definition of dev2 in src/OpenFOAM/primitives/Tensor/TensorI.H

I found the following:

$dev2(u)=u-\frac{2}{3}tr\left(u\right)$

is the rate-of-strain tensor given by

$S=\frac{1}{2}\left(\nabla u + \left(\nabla u \right)^\mathrm{T} \right)$

but according to the definition of DivDevRhoReff

$divDevRhoReff = -\nabla^{2}\left(\mu_{eff} U\right) -\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)$

And manipulating the expression (1) I conclude that the term

Code:

     + turbulence->divDevRhoReff(U)

does not correspond to (1).

If someone can help me with my confusion about this term, I was very thankful

Indeed, I was thinking it should be dev instead of dev2 as well if the explanation by poplar in http://www.cfd-online.com/Forums/ope...tml#post388688 is correct.

I hope I can find out what is wrong.

jens_klostermann · February 15, 2013, 10:07

Hi,

the term

$\nabla\cdot\left[2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) +\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) \right)\right]$
is equal to
$divDevRhoReff = -\nabla \cdot \left(\mu_{eff} \nabla U\right) -\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)$

But I miss the term
$\left(- \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right)$

in

Code:

turbulence->divDevRhoReff(U)

maybe someone can comment on this hidden term?

Jens

sasanghomi · June 14, 2013, 16:36

Hi jens
Did you find this term ? I have a similar problem .
$\left(- \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right)$

Thanks
Sasan.

jens_klostermann · June 17, 2013, 10:57

No, I didn't habe time to work further on this problem.

sharonyue · December 24, 2014, 16:48

Quote:

Originally Posted by jens_klostermann

No, I didn't habe time to work further on this problem.

I found a similar thing on this: http://www.cfd-online.com/Forums/ope...oam-2-2-x.html

pgiannatselis · February 1, 2015, 17:49

Reading http://www.cfd-online.com/Forums/ope...ivdevreff.html I concluded that this term is zero if the fluid is incompressible and near convergence it doesn't concern us. The term remains for stability reasons when we are still far from the solution. If somebody more experienced confirms my thinking, the problem is solved.

I don't feel able to tell you that my point is 100% correct.

July 14, 2012, 21:25	A question about UEqn sonicFoam	#1
lfgmarc Member Luis Felipe Gutierrez Marcantoni Join Date: Oct 2010 Location: Cordoba-Argentina Posts: 47 Rep Power: 16	Hi, I have a question about the UEqn implemented into sonicFoam, the code of the UEqn is: Code: fvVectorMatrix UEqn ( fvm::ddt(rho, U) + fvm::div(phi, U) + turbulence->divDevRhoReff(U) ); My question is about the term that is computed from the turbulence model, i.e if K-epsilon model is selected, this term results: Code: tmp<fvVectorMatrix> kEpsilon::divDevRhoReff(volVectorField& U) const { return ( - fvm::laplacian(muEff(), U) - fvc::div(muEff()dev2(fvc::grad(U)().T())) ); } Initially I thought that it corresponded to $\nabla \cdot \left( \widetilde{\tau}-\bar{\rho}\widetilde{u^{''}u^{''}} \right) = 2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) +\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) - \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right) (1)$ but after examining the definition of dev2 in src/OpenFOAM/primitives/Tensor/TensorI.H I found the following: $dev2(u)=u-\frac{2}{3}tr\left(u\right)$ is the rate-of-strain tensor given by $S=\frac{1}{2}\left(\nabla u + \left(\nabla u \right)^\mathrm{T} \right)$ but according to the definition of DivDevRhoReff $divDevRhoReff = -\nabla^{2}\left(\mu_{eff} U\right) -\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)$ And manipulating the expression (1) I conclude that the term Code: + turbulence->divDevRhoReff(U) does not correspond to (1). If someone can help me with my confusion about this term, I was very thankful __________________ Felipe G Last edited by lfgmarc; July 15, 2012 at 15:34.*

February 15, 2013, 10:07		#3
jens_klostermann Senior Member Jens Klostermann Join Date: Mar 2009 Posts: 117 Rep Power: 17	Hi, the term $\nabla\cdot\left[2\mu\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) +\left( 2\mu_{t}\left( \widetilde{S}-\frac{1}{3}\nabla\cdot\left(\widetilde{u}\right)\mathcal{I}\right) \right)\right]$ is equal to $divDevRhoReff = -\nabla \cdot \left(\mu_{eff} \nabla U\right) -\nabla \cdot \left( dev2 \left(\mu_{eff}\left(\nabla U \right)^{\mathrm{T}}\right)\right)$ But I miss the term $\left(- \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right)$ in Code: turbulence->divDevRhoReff(U) maybe someone can comment on this hidden term? Jens

June 14, 2013, 16:36		#4
sasanghomi Senior Member Sasan Ghomi Join Date: Sep 2012 Location: Denmark Posts: 292 Rep Power: 15	Hi jens Did you find this term ? I have a similar problem . $\left(- \frac{2}{3}\bar{\rho}\widetilde{k}\mathcal{I} \right)$ Thanks Sasan. immortality and franciscofelis like this.

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